1. Search for R-parity violating Supersymmetric effects in the neutron beta decay N. Yamanaka (Osaka University) 2009 年 8 月 12 日 at KEK In collaboration with T. Sato (Osaka univ.), T. Kubota (Osaka univ.) arXiv:0908.1007 [hep-ph]

2. Contents Introduction Introduction Neutron beta decay Neutron beta decay MSSM and R-parity violation MSSM and R-parity violation Neutron Beta decay within RPVMSSM Neutron Beta decay within RPVMSSM Analysis Analysis Summary Summary

3. Introduction

4. Go beyond the Standard Model Gauge group SU(3) C ×SU(2) L ×U(1) Y Gauge group SU(3) C ×SU(2) L ×U(1) Y 3 generations 3 generations 1 Higgs SU(2) L doublet 1 Higgs SU(2) L doublet quarklepton gauge bosonHiggs boson Standard Model: Reasons to go beyond the SM: Hierarchy problems Hierarchy problems Particle-antiparticle asymmetry (too many particles!) Particle-antiparticle asymmetry (too many particles!) No candidates of Dark Matter in SM No candidates of Dark Matter in SM Evidence of neutrino oscillations (1998 ～ ) Evidence of neutrino oscillations (1998 ～ ) …

5. Approach to New Physics High energy approach: Energy above the new physics threshold ⇒ create new particles Ex: LHC (CERN) Low energy approach: Very accurate experiments are now possible: ⇒ Observe the small discrepancy from SM by precise measurements of low energy phenomena precise measurements of low energy phenomena Phenomena: EDMs EDMs Decay phenomena Decay phenomena Muon g-2 Muon g-2 … … ⇒ Search for New physics beyond SM Groups: J-PARC J-PARC LANSCE LANSCE PSI PSI ILL ILL … … Neutron beta decay

6. New physics from beta decay Neutron beta decay may involve many New Physics Minimal supersymmetric standard model (MSSM) R-parity violating MSSM Left-Right symmetric model Charged Higgs exchange Leptoquark exchange … e -ud e-e-e-e- eLeLeLeL ~ ~ dRdRdRdRu e -d e-e-e-e-

7. Object R-parity violating MSSM contributes to the scalar interaction at the tree level !! Investigate RPVMSSM contribution to the neutron beta decay. Object: Recently, Measurement of R coefficient of the neutron beta decay (Kozela et al. (PSI), Phys.Rev.Lett.102, 2009) Measurement of R coefficient of the neutron beta decay (Kozela et al. (PSI), Phys.Rev.Lett.102, 2009) Bound on Fierz interference term of the beta decay (Hardy & Towner, Phys. Rev. C 79, 055502, 2009) Bound on Fierz interference term of the beta decay (Hardy & Towner, Phys. Rev. C 79, 055502, 2009) ⇒ Both give of the neutron beta decay ⇒ Both give scalar interaction of the neutron beta decay

8. Neutron beta decay

9. Process: ( ～ 100%) Interaction Hamiltonian: e - n e-e-e-e- p W V-A interaction: Standard Model e - pn e-e-e-e- eLeLeLeL ~ Scalar interaction: Exotic! Transition:

10. Angular correlations Decay distribution: Angular dependence of the beta decay Jackson, Treiman, Wyld, Nucl. Phys. 4, 206 (1957) (no polarization) (neutron polarization) (e - polarization) (neutron&e - polarization) neutrino momentum & e - polarization: ⇒ new terms!!

11. MSSM and R-parity violation

12. Supersymmetry Symmetry between boson & fermion: fermionboson ⇒ Each particle has a “super-partner” ⇔ ⇒ Phenomenological extension of the SM!! Minimal Supersymmetric Standard Model (MSSM): ⇒ Gauge invariant, renormalizable, R-parity conserving R-parity conserving particless-particles ⇔ Why SUSY? SUSY cancels power divergences (Fine tuning) SUSY can break the EW symmetry Accurate GUT at 10 16 GeV Dark matter, etc. …

13. □ □R parity violating lagrangian: R-parity violation R parity: ⇒ Conservation of baryon and lepton number in MSSM.RPVMSSM: Add R-parity violating interactions to the MSSM ud eLeLeLeL ~ L or B violating

14. Neutron beta decay within RPVMSSM

15. Steps of calculation Beta decay within R parity violating MSSM Neutron Beta decay effective interaction Angular correlation (coefficients) Plan:

16. RPV lagrangian & limits Barger, Giudice, Han, Phys. Rev. D409, 2987 (1989) Barbier et al., Phys. Rept. 420, 1 (2005) Faessler, Kovalenko, Simkovic, Phys. Rev. D58, 115004 (1998) Coupl.Current upper boundsSources λ 121 < 0.049 [m eR ]CC universality λ 131 < 0.062 [m eR ]  decay ratio λ’ 211 < 0.059 [m dR ]  decay ratio λ’ 311 < 0.11 [m dR ]  /  decay ratio λ’ 111 < 1.3 x 10 -4 [m q ] 2 [m g ] 1/2 double beta decay λ’ 112 < 0.021 [m sR ]CC universality λ’ 113 < 0.021 [m bR ]CC universality […] : sfermion mass in unit of 100 GeV ~~ RPV lagrangian: ud eLeLeLeL ~ Yukawa interaction!!

17. Neutron beta decay with R-parity violation SM contribution: Selectron exchange diagram: Down squark exchange diagram: Absorbed in V ud ⇒ Neglect ~ dRdRdRdR u e -d e-e-e-e- e -ud e-e-e-e- eLeLeLeL ~ e -d e-e-e-e-uW

18. Effective interaction (pseudoscalar interaction neglected due to non-relativistic approx) (CVC assertion) (Experiment) Effective interaction constructed from quark amplitude: Vector, axial and scalar constants: (Our work)

19. Result V-A only (SM)RPV contribution a(1- l 2 ) / (1+3 l 2 )0 b0 aRaR A2 l (1- l ) / (1+3 l 2 )0 B2 l (1+ l ) / (1+3 l 2 )(m e /E e ) la R D00 G0 H(m e / E e ) ( l 2 -1) / (1+3 l 2 )- a R K( l 2 -1) / (1+3 l 2 ) aRaR L0 aIaI N2(m e / E e ) l (1- l ) / (1+3 l 2 )- la R Q2 l (1- l ) / (1+3 l 2 ) la R R0 -la I S0 la R T0 la I U0 V-2 l (1+ l ) / (1+3 l 2 )0 W0 -la R Approx. used : Static approx. of nucleon Static approx. of nucleon Scalar & V-A interference only Scalar & V-A interference only O(m e /M N ) neglected O(m e /M N ) neglected

20. Experimental valueV-A only (SM)RPV contribution a-0.103 ± 0.004-0.1050 b(Hardy & Towner)05.12 x 10 -3 A-0.1173 ± 0.0013-0.1170 B0.981 ± 0.0040.9886.50 x 10 -3 x (m e /E e ) D(-2.8 ± 6.4 ± 3.0 ) x 10 -4 00 G0 H0.105 x (m e /E e )-5.12 x 10 -3 K0.1055.12 x 10 -3 L0 N0.056 ± 0.011 ± 0.0050.117 x (m e /E e )-6.50 x 10 -3 Q0.1176.50 x 10 -3 R0.008 ± 0.015 ± 0.00506.50 x 10 -3 S0 T0-6.50 x 10 -3 U0 V-0.9880 W0-6.50 x 10 -3

21. Analysis

22. Survey of superallowed Fermi transition J.C. Hardy, I.S. Towner, Phys. Rev. C79, 055502 (2009) In 0 + →0 + transition, effect of (real part of) scalar interaction shows up in Fierz interference term Corrected Ft value (isospin symmetry breaking correction and radiative corrections) CVC assertion ⇒ Vector interaction not renormalized Ft identical in nuclear medium for 0 + →0 + transition Fierz interference term ⇒ limit to Re(Cs) !! Test of CVC: Test of CVC with 20 superallowed 0 + →0 + beta decay.

23. R coefficient Experimental status: Final state interaction: Kozela et al.(PSI), PRL102 (2009) R exp = 0.008 ± 0.011 ± 0.005 R fsi = 0.00086 × m e /p e R SM ≦ 10 -14 Herczeg, Phys. Rev. D56 (1997) SM FSIRPV 10 -14 10 -4 10 -2 Jackson, Treiman, Wyld, Nucl. Phys. 4, 206 (1957) Exp R correlation: SM: Sensitive to the imaginary part of Cs

24. New bounds R coefficient from Kozela et al.Hardy & Towner’s work Source valueR = 0.008 ±0.011 ± 0.005b F / 2 = 0.0011 ± 0.0013 Cs /Cv-0.0184±0.0253 ± 0.01150.0011±0.0013  1i1 ’* i11 / [m eL ] 2 -0.012±0.017±0.008 (imaginary)(7.2±8.5) x 10 -4 (real) (plot with all m SUSY = 100 GeV) Current limit:

25. Summary We have investigated the R-parity violating contribution to the neutron beta decay. The following new constraints were established:

26. Future prospects D coefficient: V-A only (SM)0 Fsi O(10 -5 ) RPVMSSM0 (tree level, O(m e /m n ) contribution neglected !) L, S, T, U, W coefficients: Zero in V-A only (SM), but RPV contributions exist S,T,U,W are direct probe of the real part of scalar interaction!! Loop contribution: Non-scalar interactions at the one-loop level. ⇒ Possibility of large contribution to some angular correlations? du W e-e- e _